Calculus Calculus Math Forum

 August 10th, 2016, 07:12 AM #1 Newbie   Joined: Aug 2016 From: Ireland Posts: 2 Thanks: 0 rate of change/of a line Hi I'm studying for a calculus test I understand how to get a slope and when a number is beside an x when written as an eqution y = mx + 1 the variable for x will be the slope but in my question the slope is x^2(x squared) which is totally confusing me,can anyone help walk me through how to get the answer here is the question If two variables x and y are related by the equation y = 3x^2 – x calculate the average rate of change of y with respect to x as x varies from 3 to 5. thanks, August 10th, 2016, 07:41 AM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575 if $y = f(x) = 3x^2-x$, then the average rate of change of $f(x)$ is $\dfrac{f(5)-f(3)}{5-3}$ August 10th, 2016, 08:56 AM   #3
Math Team

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note that the average rate of change is the slope of the $\color{red}{line}$ connecting the two points on the curve ... $(3,f(3))$ and $(5,f(5))$
Attached Images avg_roc.jpg (10.2 KB, 0 views) August 10th, 2016, 09:08 AM #4 Newbie   Joined: Aug 2016 From: Ireland Posts: 2 Thanks: 0 thanks for the reply Skeether much appreciated how come we sub in both 3 and 5 I thought they are both x values? I thought we could only sub in y and x to the slope formula? thanks, August 10th, 2016, 09:33 AM #5 Math Team   Joined: Jul 2011 From: Texas Posts: 2,982 Thanks: 1575 y is a function of x ... in other words, the value of y depends on the value of x at $x = 5$, $y = f(5) = 3(5)^2 - 5$ at $x = 3$, $y = f(3) = 3(3)^2 - 3$ slope = $\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{f(5)-f(3)}{5-3}$ Last edited by skeeter; August 10th, 2016 at 09:41 AM. Tags change or of, line, rate Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post puppypower123 Calculus 1 April 14th, 2016 05:48 PM Mr Davis 97 Pre-Calculus 2 May 5th, 2014 01:57 PM bongantedd Pre-Calculus 1 April 30th, 2014 12:40 AM henoshaile Calculus 1 October 21st, 2012 10:42 PM jeff Calculus 8 February 1st, 2012 01:30 PM

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